9th LISA Symposium, Paris
ASP Conference Series, Vol. 467
G. Auger, P. Binétruy and E. Plagnol, eds.
c 2012 Astronomical Society of the Pacific
Interferometric Characterisation of Path Length Errors Resulting
from Mirror Surface Topography with Sub-nm Reproducibility
H. Kögel,1 M. Gohlke,1,2 J. Pijnenburg,3 D. Gerardi,1 T. Schuldt,4 ,U. Johann,1 C.
Braxmaier,1,5,6 and D. Weise1
1 Astrium GmbH - Satellites, 88039 Friedrichshafen, Germany
2 Humboldt University, Department of Physics, 12489 Berlin, Germany
3 TNO Opto-Mechatronics, 2600 Delft, The Netherlands
4 University of Applied Sciences Konstanz, IOS, 78462 Konstanz, Germany
5 University of Bremen, ZARM, 28359 Bremen, Germany
6 DLR German Aerospace Center, 28359 Bremen, Germany
Abstract. We present the results of our experimental characterisation of path length
errors, caused by beamwalk over the surface topography of laser mirrors. These path
length errors can have a major influence on the accuracy of the LISA measurement
instrument in Astrium’s alternative payload concept with In-Field Pointing. Our measurement setup uses a highly sensitive heterodyne interferometer for measuring the path
length error amplitudes, generated by the topography of a moving, λ/10 test mirror.
1.
Introduction
In the LISA space mission, the triangular satellite formation is subject to seasonal changes in
shape, caused by the individual orbit dynamics of its satellites. A compensation is in particular
required for angular changes of the formation. In the alternative payload concept with In-Field
Pointing (IFP), developed at Astrium GmbH, a small actuated mirror, positioned in one of the
telescope’s pupil planes, is used for this compensation (Weise et al. (2009)). During its actuation
by the In-Field Pointing Mechanism (IFPM) the laser beam scans over the surface of the optical
components in its path, which leads, due to the surface topography, to path length errors. This
paper presents a measurement setup, developed for the investigation of such surface induced
path length errors, whose results will be used for a future estimation of their noise impact in the
required picometer measurement accuracy of LISA.
2.
Measurement Setup
The used measurement setup shows some resemblance to the setups used in interferometric
profilometry and was designed to mimic path length errors caused by beamwalk across mirror
surfaces with high reproducibility. Therefore a 1 inch, λ/10 test mirror is moved perpendicular
through the outcoming measurement and reference laser beam of a heterodyne interferometer,
rising variations in the measured translation signals, due to the mirror topography. To avoid
common mode effects, caused by changes in temperature, the differential translation between
both laser beams is used for evaluation.
The heterodyne interferometer, shown in Figure 1 (left), was designed as possible concept for
the read-out of the LISA test masses and has highly symmetric optical paths (Schuldt et al.
(2009)). The beat signals of its measurement and reference laser beam are detected by Quadrant Photo Detectors (QPDs), that additionally enable tilt measurements, used for the correction
of the differential translation, falsified by small parasitic tilts of the pendulum during measurement. For the data processing a digital, FPGA based phasemeter is used, enabling measurement
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Kögel et al.
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Figure 1. Photograph of the heterodyne interferometer (left) and the pendulum
for movement of the test mirror (right).
accuracies of the setup within a few picometer in translation and a few nanoradian in tilt.
The test mirror is housed in a mirror support, mounted on a pendulum with monolithic, clearancefree hinge and a highly accurate piezo walking actuator (positioning accuracy 5 nm) for precise and highly repetitive movement. The pendulum with piezo actuator is shown in Figure 1
(right). A pre-adjustment of the pendulum’s movement is enabled by two adjustment mechanism, changing the application point and direction of the driving force. This is necessary as the
correction of the differential translation, using the tilt signal of the QPDs, is only possible for
small parasitic tilts < 1 mrad.
Measurement Results
4
2
0
-2
Translation [nm]
0
ø1300µm laser beam
500
1000 1500 2000 2500 3000 3500
4
2
Translation [µm]
Translation [nm]
3.
PSD Comparison Measurement Results
10
0
10
-5
10
-10
Interferometry (Ø13µm beam)
Microscopy (filtered, Ø13µm)
0
-2
ø13µm laser beam
0
500
1000 1500 2000 2500 3000
Travel Distance Test Mirror [µm]
10
-3
-2
-1
10
10
Spatial Frequency [1/µm]
10
0
Figure 2. Measurement results of different mirror areas, using a laser beam with
∅ ≈ 1300 µm (left, top) and ∅ ≈ 13 µm (left, bottom), as well as the PSD of the
surface topography for comparison of the results between the interferometric measurements and the comprehensive interference microscopy measurements (right).
Measurements with different beam diameters (≈ 1300 µm and ≈ 13 µm) for the measurement laser beam were performed, leading, due to the averaging of the laser light’s wavefront on
Interferometric Characterisation of Path Length Errors
299
the QPDs, to results with different lateral resolutions, shown in Figure 2 (left). The achieved
measurement results are highly reproducible with standard deviations from the mean value of
3 different measurement runs < 100 pm and show surface induced path length error amplitudes
in the range of some nanometers, which also variate with the used beam diameter.
A validation of the measurement results was realised using comprehensive surface measurements, performed by the Physikalisch Technische Bundesanstalt (PTB) in Germany. They used
interference microscopy with phase shifting as measuring method. Comparative results were
achieved by multiplying the PTB results with a filter function that simulates the ’low pass’ filter
effect for spatial frequencies of a laser beam with ∅13 µm. A filtering with a simulated laser
beam of ∅1300 µm seems at least in this case not reasonable as the measured area by interference microscopy is only 416 µm x 312 µm. The results of the comparison are shown in Figure 2
(right) as a Power Spectral Density (PSD) of the surface topography. Both measurement methods show a similar curve progression with a decline at ≈ 10−2 µm−1 , caused by the ’low pass’
filter effect of the laser beam.
4.
Conclusion and Outlook
Our measurement results demonstrate, that a beamwalk over the surface of a λ/10 test mirror
generates path length errors within some nanometers, depending on the used laser beam diameter. In the next months we will investigate their actual impact in the LISA measurement
band, considering the slow movement of the laser beam over the mirror surface in the telescope.
Therefore we are developing a theoretical model based on the measurement results demonstrated here. If it is necessary, we will realise a calibration concept of surface induced path
length errors, which should be possible with the achieved highly reproducible measurement
results.
5.
Acknowledgements
This work was funded by the DLR German Aerospace Center using recourses of the federal
ministry for economics and technology under funding code 50 OQ 0701 ”Untersuchungen zur
Systemleistung alternativer Nutzlastkonzepte für LISA”.
References
Schuldt, T., Gohlke, M., Weise, D., Johann, U., Peters, A., & Braxmaier, C. 2009, Classical and
Quantum Gravity, 26
Weise, D., Marenaci, P., Weimer, P., Schulte, H., Gath, P., & Johann, U. 2009, Journal of
Physics: Conference Series, 154